Analyse fonctionnelle et théorie des opérateurs

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1 Analyse fonctionnelle et théorie des opérateurs Objekttyp: Chapter Zeitschrift: L'Enseignement Mathématique Band (Jahr): 45 (1999) Heft 1-2: L'ENSEIGNEMENT MATHÉMATIQUE PDF erstellt am: Nutzungsbedingungen Die ETH-Bibliothek ist Anbieterin der digitalisierten Zeitschriften. Sie besitzt keine Urheberrechte an den Inhalten der Zeitschriften. Die Rechte liegen in der Regel bei den Herausgebern. Die auf der Plattform e-periodica veröffentlichten Dokumente stehen für nicht-kommerzielle Zwecke in Lehre und Forschung sowie für die private Nutzung frei zur Verfügung. Einzelne Dateien oder Ausdrucke aus diesem Angebot können zusammen mit diesen Nutzungsbedingungen und den korrekten Herkunftsbezeichnungen weitergegeben werden. Das Veröffentlichen von Bildern in Print- und Online-Publikationen ist nur mit vorheriger Genehmigung der Rechteinhaber erlaubt. Die systematische Speicherung von Teilen des elektronischen Angebots auf anderen Servern bedarf ebenfalls des schriftlichen Einverständnisses der Rechteinhaber. Haftungsausschluss Alle Angaben erfolgen ohne Gewähr für Vollständigkeit oder Richtigkeit. Es wird keine Haftung übernommen für Schäden durch die Verwendung von Informationen aus diesem Online-Angebot oder durch das Fehlen von Informationen. Dies gilt auch für Inhalte Dritter, die über dieses Angebot zugänglich sind. Ein Dienst der ETH-Bibliothek ETH Zürich, Rämistrasse 101, 8092 Zürich, Schweiz,

2 is présentée! with detailed analysis and illustrations combined with historical information. The author covers the appearance of the Gibbs phenomenon in Fourier analysis, orthogonal expan sions,intégraltransforms, splines and wavelet approximations. Methods of reducing, or filtering out, such phenomena that cover ail the above function représentations are also addressed. The book includes a thorough bibliography of some 350 références. Transformations intégrales, calcul opérationnel M.W. Wong. Un vol. relié, 16 X 24, de vin, 158 p. Universitext. Weyl transforms. ISBN Prix: DM Springer, New York, The functional analytic properties of Weyl transforms as bounded linear operators on L2(L 2 (R n ) are studied in terms of the symbols of the transforms. The boundedness, the compaetness, the spectrum, and the functional calculus of the Weyl transform are proved in détail. New results and techniques on the boundedness and compaetness of the Weyl transforms in terms of the symbols in L r (K 2n ) and in terms of the Wigner transforms of Hermite functions are given. Back groundmaterials are given in adéquate détail to enable a graduate student to proceed rapidly from the very basics to the frontier of research in an area of operator theory. Equations intégrales Donal O'Regan and Maria Meehan. Existence theory for nonlinear intégral and Mathematics and its applications, vol Un vol. relié, ISBN Kluwer Académie Prix: Dfl ,5X24,5, de 218 p. Publishers, Dordrecht, integrodifferential équations. This book présents an up-to-date account of many topics of current interest in the theory of nonlinear ordinary differential équations. They include fixed point theory, periodic problems, lower and upper surfaces, positone and semi-positone problems, singular équations, limit circle problems, finite and infinité interval problems, and impulsive differential équations. In addition many important applications are presented to complément the theory. Analyse fonctionnelle et théorie des opérateurs Banach Ernst Albrecht, Martin Mathieu, (Editors). the 13 th International Conférence on Banach Algebras, held at August 3, University of Tiibingen in Blaubeuren, July 20 Prix: DM de ix, 566 p. ISBN Proceedings of algebras '97. the Heinrich Fabri Institute of the Un vol. relié, 18X24,5, Walter de Gruyter, This volume contains refereed research articles on Banach algebras and related areas by speakers at the 13 th International Conférence on Banach algebras Parti cular topics include algebraic structure of Banach algebras, dual Banach algebras and invariant subspaces, automatic continuity, local spectral theory, algebras of analytic functions, amenability and Banach homo logyas well as applications in harmonie analysis. Some papers discuss the interplay with Fred holmtheory, differential and pseudo-differential operators, several variable spectral theory or nonassociative normed algebras. This book is of interest to researchers and graduate students in functional analysis, algebra, and topology. Operator Chebyshev splines and Kolmogorov inequalities. Sergey Bagdasarov. Un vol. relié, 17,5X24, de xm, 205 p. theory: advances and applications, vol Birkhàuser Verlag, Basel, Prix: SFr ISBN This monograph describes advances in the theory of extremal problems in classes of functions defined by a majorizing modulus of continuity a). In particular, an extensive account

3 of structural, limiting, and extremal properties of perfect co-splines generalizing stan dardpolynomialperfect splines in the theory of Sobolev classes. In this context spécial atten associated tionispaid to the qualitative description of Chebyshev w-splines and w-polynomials with the Kolmogorov problem of n-widths and sharp additive inequalities between the norms of intermediate derivatives in functional classes with a bounding modulus of continuity. Since, as a rule, the techniques of the theory of Sobolev classes are inapplicable in such classes, novel geo metricalmethodsare developed based on entirely new ideas. is given Un Second édition. Linear analysis: an introductory course. Bêla Bollobas. Cambridge Prix: ISBN vol. broché, 15x23, de xi, 240 p. University Press, Cambridge, Now revised and up-dated, this introduction to functional analysis is intended for advanced undergraduate students. The author's aim is not just to cover the standard material in a standard show the rele way, but to présent results of applications in contemporary mathematics and to vanceof functional analysis to other areas. Unusual topics covered include the geometry of finite-dimensional spaces, invariant subspaces, fixed-point theorems, and the Bishop-Phelps theorem. An outstanding feature is the large number of exercises, some straightforward, some challenging, none uninteresting. Multivalued linear operators. Ronald Cross. Un vol. relié, 16x23,5, de x, 335 p. vol US$ Marcel Dekker, Inc., New York, Pure and applied mathematics. ISBN Prix: The book describes set-valued mappings relating one subspace of a normed linear space to another... analyzes perturbation theory and stability... détails the boundedness and compactness of linear relations... uses density invariance to characterize linear relations...discusses linear sélections and dimensionality, index and coindex... outlines polar relationships and the category theorems of functional analysis... contains never-before-published material in book form on index properties in algebraic theory, closable linear relations, the theory of single-valued linear operators, partially and nowhere continuous linear relations... etc. Contributions to A. Dijksma, I. Gohberg, M. A. Kaashoek, R. Mennicken, (Editors). operator theory in spaces with an indefînite metric: the Heinz Langer anniversary volume. vi, 417 p. Un vol. relié, 17,5 X 24, de Operator theory: advances and applications, vol Prix: SFr Birkhàuser Verlag, Basel, ISBN This volume is dedicated to Heinz Langer on the occasion of his 60 th birthday. The book begins with his biography and list of publications. It contains a sélection of research papers, most of which are devoted to spectral analysis of operators or operator pencils with applications to ordinary and partial differential équations. Other papers deal with time-varying Systems, interpolation and factorization problems, and topics from mathematical physics. About half of the papers contain further developments in the theory of operators in spaces with an indefînite metric and treat new applications. The book is of interest to a wide audience of pure and applied mathematicians. F.G. Friedlander. Introduction to the theory of distributions. With addi tionalmaterial by M. Joshi.- Second édition. Un vol. broché, 15X23, de vu, 175 p. ISBN Prix: (relié: 42.50). Cambridge University Press, Cam bridge,1999. The theory of distributions is an extension of classical analysis which has acquired a parti cular importance in the field of linear partial differential équations, as well as having many

4 other applications, for example in harmonie analysis. Underlying it is the theory of topological vector spaces, but it is possible to give a systematic présentation without presupposing a know ledge,orusing more than a bare minimum, of this. This book adopts this course and is based on graduate lectures given over a number of years. In this second édition, the notion of the wave frontsetof a distribution is introduced in an additional chapter contributed by Mark Joshi. This allows many opérations on distributions to be extended and gives a much more précise unders tandingofthe nature of the singularities of a distribution. I. Gohberg, R. Mennicken, C. Tretter, (Editors). Differential and intégral operators. International Workshop on Operator Theory and Applications, IWOTA 95, in Regensburg, July 31-August 4, Operator theory: advances and applications, vol Un vol. relié, 17X24, de xn, 324 p. ISBN Prix: SFr Birkhâuser Verlag, Basel, The conférence covered différent aspects of linear and nonlinear spectral problems, starting with problems for abstract operators up to spectral theory of ordinary and partial operators, pseudodifferential operators, and intégral operators. The workshop was also focussed on operator theory in spaces with indefmite metric, operator functions, interpolation and extension problems. The applications concerned applications to mathematical physics, hydrodynamics, magnetohydrodynamics, quantum mechanics, astrophysics as well as the theory of networks and Systems. Its companion volume (OT 103), entitled Récent Progress in Operator Theory, compléments the other aspects of operator theory covered in the workshop. I. Gohberg, R. Mennicken, C. Tretter, (Editors). Récent progress in operator International Workshop on Operator Theory and Applications, IWOTA 95, theory. in Regensburg, July 31-August 4, Operator theory: advances and applications, 9 vol Un vol. relié, 17X24, de x, 283 p. ISBN Prix: SFr Birkhâuser Verlag, Basel, The papers in the two volumes of the proceedings of IWOTA 95 bring the readers up to date on récent achievements in thèse areas. This volume contains the contributions to différent aspects of operator theory and its applications. Its companion volume (OT 102), entitled Diffe rentialand Intégral Operators, is focussed especially on differential and intégral operators. The set will be of practical use to a wide-range readership in pure and applied mathematics, physics and engineering sciences. Graduate texts in Robert E. Megginson. An introduction to Banach space theory. ISBN Un vol. relié, 16x24, de xix, 596 p. mathematics, vol Prix: DM Springer, New York, The purpose of this book is to provide an introduction to the basic theory of Banach spaces and functional analysis. It prépares students for further study of both the classical works and current research. It is accessible to students who understand the basic properties of L p spaces but hâve not had a course in functional analysis. The book is sprinkled liberally with examples, historical notes, and références to original sources. Over 450 exercises provide supplementary examples and counterexamples and give students practice in the use of the results developed in the text. V.S. Sunder. spectral theory. Birkhâuser Advanced Texts. Functional analysis: ISBN Prix SFr Birkhâuser Un vol. relié, 17 X 24, de ix, 241 p. Verlag, Basel, : This book présents the concepts of functional analysis required by students of mathematics It begins with the basics of normed linear spaces and quickly proceeds to and physics.

5 concentrate on Hilbert spaces, specifically the spectral theorem for bounded as well as unbounded opérât ors in separable Hilbert spaces. While the first two chapters are devoted to basic propositions concerning normed vector spaces and Hilbert spaces, the third chapter treats advanced topics which are perhaps not standard in a first course on functional analysis (a détour into operator algebras). The fourth chapter reverts to more standard operator theory in Hilbert space, dwelling on topics such as the spectral theorem for normal operators, the polar décompo sitiontheorem,and the Fredholm theory for compact operators. Calcul des variations Andréa Braides, Anneliese Defranceschi. Homogenization of multiple intégrais. Oxford lecture séries in mathematics and its applications, vol. 12. Un vol. relié, 16,5X24, de xiv, 298 p. ISBN X. Prix: Clarendon Press, Oxford, Homogenization results and appropriate descriptive formulae are given for periodic and almost periodic functionals. Applications are described to the asymptotic behaviour of oscillating énergies describing cellular hyperelastic materials, porous média, materials with stiff and soft inclusions, and fibred média; to homogenization of Hamilton-Jacobi équations and Riemannian metrics, and to materials with multiple scales of microstructure and with multi dimensionalstructure. There is a self-contained and up-to-date introduction to the relevant results of the direct methods of F-convergence and of the theory of weak lower semi-continuous intégral functions that dépend on vector- valued fonctions. Jiirgen Jost, Xianqing Li-Jost. Calculus of variations. Cambridge studies in ad Un vol. relié, 16x23,5, de xvi, 323 p. vancedmathematics, vol. 64. ISBN Prix: Cambridge University Press, Cambridge, One-dimensional problems and classical issues like Euler-Lagrange équations are treated, as Hamilton-Jacobi theory, and in particular géodésie lines, thereby develo pingsome important géométrie and topological aspects. The basic ideas of optimal control theory are also given. The second part of the book deals with multiple intégrais. After a review of Lebesgue intégration, Banach and Hilbert space theory and Sobolev spaces (with complète détails and proofs), there is a treatment of the direct methods and the fondamental lower semi continuitytheorems. Subséquent chapters introduce the basic concepts of the modem calculus of variations, namely relaxation, Gamma convergence, bifurcation theory and minimax methods based on the Palais-Smale condition. are Noether's theorem, Géométrie Quaternions and rotation séquences: a primer with applica Un vol. relié, 20X26, de xxn, 371 p ISBN Prix: Princeton University Press, Princeton, distributed by John Wiley & Sons, Chichester, Jack B. Kuipers. tionsto orbits, aerospace, and virtual reality. In this book, the author introduces quaternions for scientists and engineers who hâve not encountered them before and shows how they can be used in a variety of practical situations The opening chapters présent introductory material and establish the book's terminology and notation. The next part présents the mathematical properties of quaternions, including quater nionalgebra and geometry. It includes more advanced spécial topics in spherical trigonometry, along with an introduction to quaternion calculus and perturbation theory. In the final section' the author discusses state-of-the-art applications.